Time-varying formation control with obstacle avoidance for fractional-order multi-agent systems

Aiming at the consensus of relative position considering obstacle avoidance for fractional-order multi-agent system, a novel distributed control algorithm is proposed in this paper. Firstly, a synthetic error of each agent under the influence of obstacles is introduced. The consensus protocols are designed based on this error according to sliding mode theory for the order increasing and decreasing, respectively. Then, the Lyapunov function is used to prove the stable convergence of the protocols. Finally, the simulation results show that the protocols can not only prevent the agents from colliding with obstacles, but also enable the agents to quickly recover the expected formation and achieve consensus of the relative position.